lift sheaves are pivotally connected to a frame element which may comprise car frame cross-head channels connected to a lift car or an overhead beam fixed in a lift well to facilitate movement of the lift car in the lift well. The rotatable hitch allows the lift sheave to be oriented into a desired orientation relative to the frame member during installation and also allows a very slight amount of rotation of the lift sheave relative to the frame elements during use, dependent upon the load applied by a cable as the cable is wound onto and wound off the lift sheave, particularly at the extremities of the movement of the lift car. This angle of movement may be as small as 1.degree.. Some Government regulations also require the rotatable hitch to be secured at two locations to provide for failsafe connection in the event that one of the couplings of the sheave fails during use of the lift.